Uniform superconvergence analysis of Ciarlet‐Raviart scheme for Bi‐wave singular perturbation problem

Abstract

Uniform superconvergence analysis of the Ciarlet‐Raviart mixed finite element scheme is discussed for solving the fourth‐order Bi‐wave singular perturbation problem (SPP) by the bilinear element. Firstly, the existence and uniqueness of the approximation solution are proved. Secondly, with the help of the special characters of this element, uniform superclose result of order O(h2) for the original variable in H1 norm and uniform optimal order estimate of order O(h2) for the intermediate variable in L2 norm are deduced with respect to the real perturbation parameter δ appearing in the considered problem. Furthermore, the global uniform superconvergent estimate is obtained through the interpolated postprocessing approach. Finally, some numerical results are provided to verify the theoretical analysis. Here, h denotes the mesh size.